Does increasing Blender's noise texture increase the quality of the rendered video?
Short answer: it depends on your intentions and on the scene. Just try different settings.

Longer answer: the noise detail is not a quality setting, you might want a "blurry" look. And even if you prefer the "rough" look, it might not matter depending on the scene (for example if your object is far away from the camera). 

Note that creating a more detailed noise requires more computing time. It depends on your scene whether this extra time is significant.

The scale is not related to the detail (or to the quality), the best scale depends only on your intentions. The scale setting should not influence the rendering time.